## Hydrogen to Heavy Metal Ratio (H/HM ratio)

Posted by Syeilendra Pramuditya on May 4, 2009

Hydrogen to Heavy Metal Ratio or H/HM for short, is a typical parameter in neutronic analysis of nuclear reactor, or more specifically, the Pressurized Water Reactor (PWR) type. Basically it is simply the ratio of moderator (water) to fuel/fissile material (U/Pu/Th) within one calculation cell. I will briefly show you how to calculate this H/HM.

Consider a standard Westinghouse PWR fuel: cylindrical fuel rod array, arranged in rectangular geometry, please refer to this link for the detail of its technical specifications.

Next, make sure that you have understood how to calculate the atomic number density, or otherwise learn it first from the following link:

Now suppose that the fuel has enrichment level of 3%, and 95% theoretical density, hence the atomic number densities are as follow:

Atomic number density of Uranium in the fuel: N_{U} = N_{U235} + N_{U238} = 2.3227E+22 atoms/cc

Atomic number density of Hydrogen in the moderator (water): N_{H} = 3.3456E+22 atoms/cc

And the volume fractions are as follow:

Fuel : 33.501 %

Coolant : 54.943 %

Structure : 11.555 %

And finally the H/HM ratio is calculated as follow:

That’s all, easy huh..?

## Lars said

does a H/HM ratio of 2.36 make sense?

https://syeilendrapramuditya.wordpress.com/2009/05/04/hydrogen-to-heavy-metal-ratio-hhm-ratio/

if you state that the H/HM ratio is 3.4?

https://syeilendrapramuditya.wordpress.com/2009/04/ when

I think 3.4 is correct but using your numbers I get about 2.36, too.

Syeilendra says..Hi Lars,

Yes it does make sense, as you can see in this post, H/HM ratio depends on atomic number density and volume fraction, in which atomic number density depends on enrichment level. In this post, the enrichment level is 3% U235 (typical value for conventional PWR), and you will get H/HM = 2.36.

H/HM = 3.4? are you talking about the IRIS reactor? https://syeilendrapramuditya.wordpress.com/2009/04/14/the-iris-reactor-technical-specifications/

IRIS reactor design uses the same fuel assembly as that of conventional Westinghouse PWR (which means same volume fractions with the values shown in this post), but it uses slightly higher enrichment level: 4.95% U235. When you calculate atomic number density by using this value, you will get:

N(H)=4.8771E+22

N(HM)=N(U235+U238)=2.34772E+22

*Atomic number density>> http://www.scribd.com/doc/23700937/Atomic-Number-Density

If you use those values, you will get H/HM = 3.4

Hope it helps